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In a medical experiment concerning 12 patients with a certain type of ear condition, the following measurements were made for blood flow ()) and auricular pressure (x): 8.5 9.8 10.8 11.5 11.2 9.6 10.1 13.5 14.2 11.8 8.7 6.8 3 12 10 14 7 13 17 10 5 5 Er =126.5 Er- =1,381.85 Ev =1 13 Ey= =1,251 Exy =1,272.2 (1) Construct a scatterplot of blood flow against auricular pressure and comment briefly on any relationship between them. [3] (ii] Calculate the equation of the least-squares fitted regression line of blood flow on auricular pressure. [4] (iii) (a) Use a suitable pivotal quantity with a : distribution to show how to derive the usual 95% confidence interval for the slope coefficient of the underlying regression line, and calculate the interval. (b) Use your calculated confidence interval to comment on the hypothesis that the true underlying slope coefficient is equal to 1 5 [5] (iv) (a) Use a suitable pivotal quantity with a y' distribution to derive a 95% confidence interval for the underlying error variance of, and calculate the interval. (b) Hence calculate a 95% confidence interval for the error standard deviation o. [5] [Total 17]Population censuses in a certain country are taken each year on the President's birthday, provided that the President's astrological advisor deems the taking of a census favourable. Censuses record the age of every inhabitant in completed years (that is, carrare age). Deaths in this country are registered as they happen, and classified according to age nearest birthday at the time of death. Below are some data from the three most recent censuses. Age in Population Population Population completed 2006 2009 2010 Years (thousands) (thousands) (thousands) G4 300 320 350 65 290 310 330 GG 280 300 320 Between the censuses of 2006 and 2009 there were a total of 3,000 deaths to inhabitants aged 65 nearest birthday, and between the censuses of 2009 and 2010 there were a total of 1,000 deaths to inhabitants aged 65 nearest birthday. (1) Estimate, stating any assumptions you make, the death rate at age 65 years for each of the following periods: the period between the 2005 and 2009 censuses the period between the 2009 and 2010 censuses [6] (ii) Explain the exact age to which your estimates apply. [1] [Total 7]